What defines a cluster that has reached a virialized dynamic state?

Kinetic energy equals potential energy, achieving gravitational stability

A virialized cluster represents a mature, dynamically relaxed system that has settled down over billions of years following its initial gravitational collapse. This state is characterized by a specific energetic balance where the average kinetic energy of the system's components (galaxies, gas) is in equilibrium with the total gravitational potential energy. When this condition is met, the cluster is considered gravitationally stable and bound, meaning it is no longer undergoing rapid contraction or violent expansion. Structurally, virialized clusters typically exhibit smoother X-ray emission profiles and possess a more regular, often spherical or ellipsoidal, shape, in contrast to the irregular structures seen in merging systems.